A prolongation structure for the AKNS system and its generalization

1977 ◽  
Vol 18 (3) ◽  
pp. 533-536 ◽  
Author(s):  
H. C. Morris
Keyword(s):  
Akns System ◽  
Prolongation Structure

Bilinear approach to supersymmetric AKNS system; multiple dressing of fermionic amplitudes

2020 ◽  
Vol 35 (17) ◽  
pp. 2050143 ◽  
Author(s):  
Corina N. Babalic ◽  
A. S. Carstea
Keyword(s):  
Bilinear Form ◽  
Tau Function ◽  
Bilinear Formalism ◽  
Akns System ◽  
Bilinear Approach

In this paper, we investigate the super-bilinear formalism and interaction of supersoliton solutions for the supersymmetric AKNS system [H. Aratyn and A. Das, Mod. Phys. Lett. A 13, 1185 (1998)]. It is shown that the super-bilinear form involves an auxiliary fermionic tau function and the supersolitons have less freedom than expected (concerning the dependence on fermionic parameters). Also, the interaction between super-solitons is much more complicated than in the case of real supersymmetric equations (KdV, mKdV, Sawada–Kotera, Sine–Gordon, etc.), involving four types of dressing of the fermionic parameters. These solutions are general compared to the ones found in Ref. 1 which contain no fermionic parameter.

Riemann–Hilbert problems of a nonlocal reverse-time six-component AKNS system of fourth order and its exact soliton solutions

2021 ◽  
pp. 2150035
Author(s):  
Alle Adjiri ◽  
Ahmed M. G. Ahmed ◽  
Wen-Xiu Ma
Keyword(s):  
Fourth Order ◽  
Soliton Solutions ◽  
Reverse Time ◽  
Akns Hierarchy ◽  
Spectral Problems ◽  
Jump Matrix ◽  
Akns System ◽  
Associated Matrix ◽  
Time Reduction ◽  
Exact Soliton Solutions

We investigate the solvability of an integrable nonlinear nonlocal reverse-time six-component fourth-order AKNS system generated from a reduced coupled AKNS hierarchy under a reverse-time reduction. Riemann–Hilbert problems will be formulated by using the associated matrix spectral problems, and exact soliton solutions will be derived from the reflectionless case corresponding to an identity jump matrix.

Complete Integrability Prolongation Structure and Backlund Transformation for the Konno-Onno Equation

2000 ◽  
Vol 55 (5) ◽  
pp. 545-549
Author(s):  
Chandan Kr. Das ◽  
A. Roy Chowdhury
Keyword(s):  
Positive Result ◽  
Explicit Form ◽  
Bäcklund Transformation ◽  
Lax Pair ◽  
Independent Study ◽  
Complete Integrability ◽  
Painlevé Test ◽  
Backlund Transformation ◽  
Prolongation Structure ◽  
Prolongation Theory

Abstract Painleve analysis is used to study the complete integrability of the recently proposed Konno-Onno equation, which also leads to a general form of solutions of the system. An independent study, using the prolongation theory, gives the explicit form of the Lax pair which is then used to obtain the Backlund transformation connecting two sets of solutions of the system. The existence of the Lax pair and the positive result of the Painleve test indicate the complete integrability of the system

scholarly journals Symmetry Analysis, Bäcklund Transformations, and Interaction Solutions for an AB Modified KdV System

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Man Jia
Keyword(s):  
Symmetry Reduction ◽  
Symmetry Analysis ◽  
Bäcklund Transformations ◽  
Cnoidal Waves ◽  
Nonlocal Symmetries ◽  
Interaction Solutions ◽  
Backlund Transformations ◽  
Akns System ◽  
Finite Transformation ◽  
Truncated Painlevé Expansion

An AB modified KdV (AB-mKdV) system which can be used to describe two-place event is studied in this manuscript. Because the AB-mKdV system is considered as a special reduction of the famous AKNS system, the properties of the AKNS system are first revealed by using symmetry analysis. The nonlocal symmetries related to truncated Painlevé expansion, the finite transformation, and the symmetry reduction solutions of the AKNS system are presented. The corresponding Bäcklund transformations and the interaction solutions of the AB-mKdV system are constructed based on the special reduction. The results demonstrate that the AB-mKdV system possesses many kinds of interaction solutions, such as the interactions between kink and soliton and kink and cnoidal waves. The soliton can be changed from bright to dark during propagation.

scholarly journals BINARY NONLINEARIZATION OF THE SUPER AKNS SYSTEM

2008 ◽  
Vol 22 (04) ◽  
pp. 275-288 ◽  
Author(s):  
JINGSONG HE ◽  
JING YU ◽  
YI CHENG ◽  
RUGUANG ZHOU
Keyword(s):  
Hamiltonian System ◽  
Spectral Problem ◽  
Integrable Hamiltonian System ◽  
Integrals Of Motion ◽  
Finite Dimensional ◽  
Akns System ◽  
Hamiltonian Forms

We establish the binary nonlinearization approach of the spectral problem of the super AKNS system, and then use it to obtain the super finite-dimensional integrable Hamiltonian system in the supersymmetry manifold ℝ4N|2N. The super Hamiltonian forms and integrals of motion are given explicitly.

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